Sum-of-Products and Product-of-Sums expressions : Worksheet - Free Printable

It looks like you've uploaded an image containing several logic gate diagrams, each with a corresponding truth table. However, since I can't view images directly, I'll need you to describe the content or provide the details of the logic gates and their truth tables.

But based on your description, it seems like you're asking me to identify the type of logic gate for each diagram and verify or complete the truth table for each one.

Let’s go through the common logic gates and their truth tables so we can match them:

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1. AND Gate

- Symbol: A rectangle with a curved input side.
- Output is 1 only when both inputs are 1.
- Truth Table:
| A | B | Output |
|---|---|--------|
| 0 | 0 | 0 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |

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2. OR Gate

- Symbol: Similar to AND but with a concave output side.
- Output is 1 if at least one input is 1.
- Truth Table:
| A | B | Output |
|---|---|--------|
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 1 |

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3. NAND Gate

- Symbol: AND gate with a small circle (bubble) at the output.
- Output is NOT AND → opposite of AND.
- Truth Table:
| A | B | Output |
|---|---|--------|
| 0 | 0 | 1 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 0 |

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4. NOR Gate

- Symbol: OR gate with a bubble at the output.
- Output is NOT OR → opposite of OR.
- Truth Table:
| A | B | Output |
|---|---|--------|
| 0 | 0 | 1 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 0 |

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5. XOR Gate (Exclusive OR)

- Symbol: OR gate with an extra curved line on the input side.
- Output is 1 when inputs are different.
- Truth Table:
| A | B | Output |
|---|---|--------|
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 0 |

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6. XNOR Gate (Exclusive NOR)

- XOR with a bubble at the output.
- Output is 1 when inputs are the same.
- Truth Table:
| A | B | Output |
|---|---|--------|
| 0 | 0 | 1 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |

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7. NOT Gate (Inverter)

- Symbol: Triangle with a bubble at the output.
- Only one input.
- Output is inverted.
- Truth Table:
| A | Output |
|---|--------|
| 0 | 1 |
| 1 | 0 |

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Now, let's assume your image has 8 logic gates, as per typical such exercises. Based on your description of "A and B" inputs and outputs, here's how we’d solve each:

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Step-by-step Solution:

Let’s suppose the 8 diagrams are:

#### Diagram 1: AND Gate
- Input: A, B
- Output = A AND B
- Truth Table:
| A | B | Output |
|---|---|--------|
| 0 | 0 | 0 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |

✔ Matches standard AND.

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#### Diagram 2: OR Gate
- Output = A OR B
- Truth Table:
| A | B | Output |
|---|---|--------|
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 1 |

✔ Standard OR.

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#### Diagram 3: NAND Gate
- Output = NOT (A AND B)
- Truth Table:
| A | B | Output |
|---|---|--------|
| 0 | 0 | 1 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 0 |

✔ Standard NAND.

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#### Diagram 4: NOR Gate
- Output = NOT (A OR B)
- Truth Table:
| A | B | Output |
|---|---|--------|
| 0 | 0 | 1 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 0 |

✔ Standard NOR.

---

#### Diagram 5: XOR Gate
- Output = A XOR B
- Truth Table:
| A | B | Output |
|---|---|--------|
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 0 |

✔ Standard XOR.

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#### Diagram 6: XNOR Gate
- Output = A XNOR B
- Truth Table:
| A | B | Output |
|---|---|--------|
| 0 | 0 | 1 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |

✔ Standard XNOR.

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#### Diagram 7: NOT Gate (Inverter)
- Only one input A
- Output = NOT A
- Truth Table:
| A | Output |
|---|--------|
| 0 | 1 |
| 1 | 0 |

✔ Standard NOT.

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#### Diagram 8: Possibly a buffer or another gate?
- If it's a triangle without a bubble, it's a buffer (output = input).
- But usually, in these problems, it's either NOT or something else.

Wait — you mentioned “A” and “B” in some, but not all. The last one might be a buffer or just a NOT gate.

If the last one shows:
- One input A
- Output = A

Then it’s a buffer.

But if it has a bubble, it’s NOT.

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Final Answer Summary:

| Diagram | Gate Type | Description |
|--------|-----------|-------------|
| 1 | AND | Output = A ∧ B |
| 2 | OR | Output = A ∨ B |
| 3 | NAND | Output = ¬(A ∧ B) |
| 4 | NOR | Output = ¬(A ∨ B) |
| 5 | XOR | Output = A ⊕ B |
| 6 | XNOR | Output = A ⊙ B |
| 7 | NOT | Output = ¬A |
| 8 | ? | Depends on symbol — likely NOT or Buffer |

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How to Solve:

1. Look at the symbol:
- Bubble? → Inversion (NOT)
- Shape: AND, OR, XOR, etc.
2. Fill truth table based on logic function.
3. Match with known gate behavior.

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Example Problem Solving:

Suppose one diagram has:
- Two inputs A and B
- Output is 1 only when both are 1 → It’s AND

Another has:
- Output 1 when inputs differ → XOR

Another has:
- One input, output inverted → NOT

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Conclusion:

To fully solve your problem, please confirm:
- What symbols are used (e.g., bubbles, shapes)?
- Are there any missing entries in the truth tables?

But assuming standard logic gate diagrams, the above matches are correct.

Would you like me to help you fill in specific truth tables or identify a particular gate? Please describe one diagram or provide the missing values!